Viscoelasticity expression and extension of seismic dispersion and attenuation in porous media with multiple fracture sets

Abstract

Intensive studies have been conducted on fluid-related seismic dispersion and attenuation in saturated anisotropic media. Most of the studies are concentrated on the transversely isotropy media. However, the fractures distribution in subsurface reservoirs is often complex. When there are multiple fracture sets developing in a porous background, the signatures of seismic dispersion and attenuation remain unclear. In this paper, we propose a method to calculate the frequency-dependent stiffness matrix of a porous medium with multiple fractures sets from a perspective of viscoelasticity. Due to the favorable approximation performance of the generalized standard linear solid model and Chapman model, we use a modified form of generalized standard linear solid model to simulate the frequency-dependent stiffness tensor of porous media with multiple fracture sets. The representation of the stiffness tensor utilizes the modulus defect to denote the effects the fractures including fracture density and geometry. With the procedure of calculating the stiffness tensors at low- and high-frequency limits, we can easily calculate the frequency-dependent stiffness tensor for media with multiple fracture sets with arbitrary orientations and directions. We then analyze the effects of the fracture parameters on the viscoelasticity characteristics taking orthotropic medium as an example. The results can help to understand the viscoelasticity and the mesoscopic seismic attenuation associated with fractures and fluids and can provide a practical rock physics model when dealing with reservoirs with complex fracture patterns.

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Fig. 1

[Modified from Lan (2014)]

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The codes concerned in the manuscript are available.

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Funding

National Natural Science Foundation of China (No. 41674139).

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Correspondence to Jinwei Zhang.

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Zhang, J., Ding, R., Zhao, L. et al. Viscoelasticity expression and extension of seismic dispersion and attenuation in porous media with multiple fracture sets. Acta Geophys. (2020). https://doi.org/10.1007/s11600-020-00497-y

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Keywords

  • Fractured reservoirs
  • Seismic rock physics
  • Dispersion and attenuation
  • Viscoelasticity